Solve for $x$ and $y$ using elimination. ${3x+y = 14}$ ${-5x-y = -22}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $-2x = -8$ $\dfrac{-2x}{{-2}} = \dfrac{-8}{{-2}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {3x+y = 14}\thinspace$ to find $y$ ${3}{(4)}{ + y = 14}$ $12+y = 14$ $12{-12} + y = 14{-12}$ ${y = 2}$ You can also plug ${x = 4}$ into $\thinspace {-5x-y = -22}\thinspace$ and get the same answer for $y$ : ${-5}{(4)}{ - y = -22}$ ${y = 2}$